On a weak type (1,1) inequality for a maximal conjugate function
Volume 125 / 1997
Studia Mathematica 125 (1997), 13-21 DOI: 10.4064/sm-125-1-13-21
In their celebrated paper , Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of $H^p$ spaces for 0 < p < ∞. In the present paper, we show that the methods in  extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.